Solved Assignment 2 - Principles of Electronic Devices 1 | ECEN 5355, Assignments of Electrical and Electronics Engineering

Download Solved Assignment 2 - Principles of Electronic Devices 1 | ECEN 5355 and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! 1.8 An electron is moving in a piece of lightly doped silicon under an applied field at 27oC so that its drift velocity is one-tenth of the thermal velocity. Calculate the average number of collisions it will experience in traversing by drift a region 1 μm wide. What is the voltage applied across this region? The drift velocity is obtained by calculating the thermal velocity using the effective mass for conductivity calculations: 31 23 * 101.926.0 3001038.13 10 13 10 1 10 − − ×× ××× === e th d m kTvv = 22.9 km/s The transist time is obtained from the length of the region divided by the drift velocity 3 6 109.22 10 × == − d r v Lt = 43.7 ns The collision time is obtained from the mobility 19 31* 106.1 101.926.01414.0 − − × ××× == q men c μ τ = 0.21 ps The number of collisions is therefore tr/τc = 209 The electric field equals: 1414.0 109.22 3× == n dv μ E =162 kV/m and the applied voltage equals E x L = 0.162 V 1.10The electron concentration in a piece of uniform, lightly doped, n-type silicon at room temperature varies linearly from 1017 cm-3 at x = 0 to 6 x 1016 cm-3 at x = 2 μm. Electrons are supplied to keep this concentration constant with time. Calculate the electron current density in the silicon if no electric field is present. Assume μn = 1000 cm2/V-s and T = 300 K. 2019 102)(9.25106.1 ×−×××=+= − dx dnqDnEqJ nnμ = -828 A/cm 2 1.12(Dielectric relaxation in solids) Consider an homogenous one-carrier conductor of conductivity σ and permittivity ε. Imagine a given distribution of the mobile charge density ρ(x, y, z; t = 0) in space at t = 0. We know the following facts from electro-magnetism, provided we neglect diffusion current: ρ=∇D rr , E rr ε=D , E rr σ=J , dt dJ ρ−=∇ rr a) Show from these facts that ρ(x, y, z; t) = ρ(x, y, z; t = 0) e-t/(ε/σ). This result shows that uncompensated charge cannot remain in a uniform conducting material, but must accumulate at discontinuous surfaces or other places of non-uniformity.